An exact integral equation for the renormalized Fermi surface

The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counter-term which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counter-term.